From MLE to Bayesian Inference: Why Your Estimate...

In the MLE tutorial, we estimated a coin's bias by finding the single parameter value that maximises the likelihood. Flip a coin 3 times, get 3 heads, and MLE says $\hat{\theta} = 1.0$ — the coin always lands heads. That feels wrong. With only 3 flips, we shouldn't be certain of anything. The problem isn't the likelihood — it's that MLE gives you a point estimate with no way to express doubt. Bayesian inference fixes this by computing an entire distribution over parameter values, weighted by how